Related papers: Reconstruction of FRI Signals using Deep Neural Ne…
Finite Rate of Innovation (FRI) sampling theory enables reconstruction of classes of continuous non-bandlimited signals that have a small number of free parameters from their low-rate discrete samples. This task is often translated into a…
A spatial signal is defined by its evaluations on the whole domain. In this paper, we consider stable reconstruction of real-valued signals with finite rate of innovations (FRI), up to a sign, from their magnitude measurements on the whole…
Finite-rate-of-innovation (FRI) signals are ubiquitous in applications such as radar, ultrasound, and time of flight imaging. Due to their finite degrees of freedom, FRI signals can be sampled at sub-Nyquist rates using appropriate sampling…
In this paper, we consider the problem of recovering a sum of filtered Diracs, representing an input with finite rate of innovation (FRI), from its corresponding time encoding machine (TEM) measurements. So far, the recovery was guaranteed…
In this paper, we consider the problem of estimating finite rate of innovation (FRI) signals from noisy measurements, and specifically analyze the interaction between FRI techniques and the underlying sampling methods. We first obtain a…
We propose a two-stage algorithm for the super-resolution of MR images from their low-frequency k-space samples. In the first stage we estimate a resolution-independent mask whose zeros represent the edges of the image. This builds off…
Neuromorphic sampling is a bioinspired and opportunistic analog-to-digital conversion technique, where the measurements are recorded only when there is a significant change in the signal amplitude. Neuromorphic sampling has paved the way…
Finite rate of innovation (FRI) is a powerful reconstruction framework enabling the recovery of sparse Dirac streams from uniform low-pass filtered samples. An extension of this framework, called generalised FRI (genFRI), has been recently…
Reconstruction of magnetic resonance imaging (MRI) data has been positively affected by deep learning. A key challenge remains: to improve generalisation to distribution shifts between the training and testing data. Most approaches aim to…
This paper presents a novel approach for estimating the modes of an observed non-stationary mixture signal. A link is first established between the short-time Fourier transform and the sparse sampling theory, where the observations are…
Pruning is a model compression method that removes redundant parameters in deep neural networks (DNNs) while maintaining accuracy. Most available filter pruning methods require complex treatments such as iterative pruning, features…
Finite Rate of Innovation (FRI) sampling techniques provide efficient frameworks for reconstructing signals with inherent sparsity at rates below Nyquist. However, traditional FRI reconstruction methods rely heavily on pre-defined kernels,…
The Deep Fourier Residual (DFR) method is a specific type of variational physics-informed neural networks (VPINNs). It provides a robust neural network-based solution to partial differential equations (PDEs). The DFR strategy is based on…
We develop a method for the accurate reconstruction of non-bandlimited finite rate of innovation signals on the sphere. For signals consisting of a finite number of Dirac functions on the sphere, we develop an annihilating filter based…
We study recovery of amplitudes and nodes of a finite impulse train from noisy frequency samples. This problem is known as super-resolution under sparsity constraints and has numerous applications. An especially challenging scenario occurs…
Phase retrieval consists in the recovery of an unknown signal from phaseless measurements of its usually complex-valued Fourier transform. Without further assumptions, this problem is notorious to be severe ill posed such that the recovery…
In functional MRI (fMRI), faster acquisition via undersampling of data can improve the spatial-temporal resolution trade-off and increase statistical robustness through increased degrees-of-freedom. High quality reconstruction of fMRI data…
We introduce a new class of iterative image reconstruction algorithms for radio interferometry, at the interface of convex optimization and deep learning, inspired by plug-and-play methods. The approach consists in learning a prior image…
We consider synthetic aperture radar imaging of a region containing point-like targets. Measurements are the set of frequency responses to scattering by the targets taken over a collection of individual spatial locations along the flight…
We present a sampling theory for a class of binary images with finite rate of innovation (FRI). Every image in our model is the restriction of $\mathds{1}_{\{p\leq0\}}$ to the image plane, where $\mathds{1}$ denotes the indicator function…